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Rational polygons

Published online by Cambridge University Press:  26 February 2010

D. E. Daykin
D. E. Daykin
Affiliation:
The University, Reading
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Extract

Following A. S. Besicovitch [1] and L. J. Mordell [3], we say that a polygon is rational if the lengths of all its sides and diagonals are rational. Besicovitch proved that the set of all rational right-angled triangles is dense in the set of all right-angled triangles and that the set of all rational parallelograms is dense in the set of all parallelograms. Then Mordell showed that the set of all rational quadrilaterajs is dense in the set of all quadrilaterals.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 2 , December 1963 , pp. 125 - 131
Copyright
Copyright © University College London 1963

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References

1.Besicovitch, A. S., “Rational polygons”, Mathematika, 6 (1959), 98.CrossRefGoogle Scholar
2.Dickson, L. E., History of the theory of numbers, Vol. II (Washington, 1920).Google Scholar
3.Mordell, L. J., “Rational quadrilaterals”, J. London Math. Soc., 35 (1960), 277–282.CrossRefGoogle Scholar
4.Nagell, T., “Solution do quelque problèmes dans la théorie arithmetiquo des cubiques planes du premier genre”, Vid. Akad. Skrifter. Oslo, I (1935), No. 1.Google Scholar
5.Skolem, Th., Diophantische Gleichungen (Berlin, 1938).Google Scholar